Annals of Botany 77 : 235–242, 1996
An Analysis of the Relation between Dry Matter Allocation to the Tuber
and Earliness of a Potato Crop
P. L. K O O M AN*† and R. R A B B I N GE*
* DLO-Research Institute for Agrobiology and Soil Fertility (AB-DLO), P.O. Box 14, 6700 AA Wageningen
and † Department of Theoretical Production Ecology, Wageningen Agricultural UniŠersity, P.O. Box 430,
6700 AA Wageningen, The Netherlands
Received : 25 April 1995
Accepted : 11 October 1995
Compared with late cultivars, early potato cultivars allocate a larger part of the available assimilates to the tubers
early in the growing season, leading to shorter growing periods and lower yields. A dynamic simulation model,
integrating effective temperature and source–sink relationships of the crop, was used to analyse this relation, using
data from experiments in the Netherlands carried out over 5 years. Dry matter allocation to the tuber in these field
experiments was simulated well when the tuber was considered as a dominant sink that affects earliness of a potato
crop in two ways : early allocation of assimilates to the tubers stops foliage growth early in the season and reduces
the longevity of individual leaves. In a sensitivity analysis the influence of tuber initiation, leaf longevity and the
maximum relative tuber growth rate (Rtb) on assimilate allocation and crop earliness was evaluated. It was found that
the maximum relative tuber growth rate can influence crop earliness more than the other two factors, but when
conditions for tuber growth are optimal, the leaf longevity is most important.
# 1996 Annals of Botany Company
Key words : Solanum tuberosum L., simulation model, source–sink relationships, cultivars.
INTRODUCTION
Potato contributes significantly to the quality and quantity
of the diet because of its high vitamin C and protein content
and it is grown in various climates throughout the world
(Haverkort, 1990). Potato is now being grown successfully
in tropical and subtropical climates ; potato production has
doubled in these regions since the late 1960s (Zaag and
Horton, 1983). However, the crop is mainly grown in
relatively cool temperate or tropical highland climates
and seems to be poorly adapted to warm climates. Tuber
yields in warm regions still vary widely (Haverkort, 1986).
The poor adaptation of potato may be caused by an
unfavourable allocation of assimilates within the plant,
since temperatures above 23 °C favour allocation of dry
matter to the foliage at the cost of tuber growth (Haverkort
and Harris, 1987).
Differences in assimilate allocation in potato are often
referred to as earliness, because a difference in life span of
the crop is observed in the field (Heemst, 1986 ; Spitters,
1987). Assimilate allocation results from the interaction of
climatic conditions, cultural practices and genotype. Bodlaender (1960) showed that short photoperiod and low
temperatures promote crop earliness. Heemst (1986) demonstrated that reduced nitrogen application and larger seed
size made a crop earlier and Perrenec and Madec (1980)
showed that older seed tubers have a similar effect. The
cultivars in the existing gene pool exhibit a great diversity of
assimilate allocation patterns (Heemst, 1986).
Assimilate allocation is the result of growth and de0305–7364}96}030235­08 $18.00}0
velopment which are mutually dependent and are difficult to
analyse separately in experiments. Lateral stems, for
example, do not develop when there is a shortage of
available carbohydrate ; in this case, development is restricted by growth. On the other hand, unless the appropriate
conditions have been met, tubers will not be initiated even
though sufficient assimilates are available for tuber growth.
Here growth is restricted by development.
A quantitative approach using a combination of models
and experiments allows the interaction between growth and
development of the potato crop to be studied. The growth
of the potato crop has been studied extensively, and various
models are available to describe or predict the total biomass
when environmental parameters are known (Ng and
Loomis, 1984 ; Spitters, 1987 ; Ingram and McCloud, 1984).
However, the influence of external factors and genotype on
assimilate allocation and earliness in potato is poorly
understood and is therefore not included in these models.
The aim of the study described in this paper was to
analyse the influence of assimilate allocation on the earliness
of potatoes grown in field experiments. This relation was
studied with a dynamic simulation model, integrating
temperature and source–sink relationships at the crop level.
MATERIAL AND METHODS
Some definitions
Effective temperature is defined as the average daily
temperature above the base temperature of 2 °C. A daily
# 1996 Annals of Botany Company
236
Kooman and Rabbinge—Tuber Dry Matter Allocation and Potato Crop Earliness
leaf class is the amount of leaf (kg ha−") formed in 1 d. Crop
earliness is the life span of a crop (d), leaf longevity is the
maximum life span of a daily leaf class, expressed as °Cd
above 2 °C. Tuber initiation date is defined as the date on
which actual tuber growth starts. In the model an initial
value of 10 kg dry matter ha−", estimated from tuber growth
curves is taken as the starting point. The sink strength of the
tuber (kg ha−" d−") is defined as the ability to compete for
assimilates compared to other organs. Assimilate allocation
is the part of the daily assimilate production allocated to a
particular organ.
Intercepted light
LUE
Senescence
rate
Daily growth
The data
Experimental data sets to evaluate assimilate allocation
should meet the following prerequisites : the experiments
must be carried out under conditions which do not limit
growth. There should be no shortage of water and fertilizer,
as assimilate allocation is influenced by water and nutrient
shortage (Spitters and Schapendonk, 1990). Periodic harvests should be carried out during the growing season to
monitor dry matter accumulation and allocation during the
season. Cultivars of different maturity classes should be
included, so that the influence of assimilate allocation on
crop earliness can be evaluated. Data from two such sets of
experiments were available at the DLO Research Institute
for Agrobiology and Soil Fertility, Wageningen, The
Netherlands ; they have been extensively described by
Gmelig Meyling and Bodlaender (1981, set 1) and Caesar
et al. (1981, set 2).
Both sets of data are from cultivar trials, carried out on
a sandy soil with a high organic matter content at Varsseveld
(East Netherlands). Set 1 is from trials carried out in 1968
and 1969 and involving the cultivars Alpha, Irene, Mentor,
Pimpernel and Prudal. These cultivars ranged from very
early (Prudal) to very late (Pimpernel). Set 2 is from trials
carried out in 1971, 1972 and 1973 with four cultivars : the
early cultivars Rheinhort and Ostara and the late Alpha and
Condea. Nitrogen was applied at 200 kg ha−" before planting
and the planting density was 6¬10% plants ha−" in set 1 and
4¬10% plants ha−" in set 2. The distance between the rows
was 75 cm in both sets. Periodic harvests of ten plants were
carried out at two-weekly intervals from May to Sep. Plants
were divided into four fractions : tubers, stems (above and
below ground part), leaves (the whole compound leaves
including petioles) and below ground parts (recovered roots
and stolons), and the fresh and dry weights of each fraction
were determined separately. The leaf area index was
determined from the leaf dry matter, using a specific leaf
area of 300 cm# g−". The dry matter allocation was determined by dividing the growth of a specific organ between
two harvests by the growth of the total plant.
The model
The model used in this study was relatively simple and
focused on assimilate allocation, regulated by a dominant
tuber sink (Moorby, 1970 ; Sale, 1973 ; Gawronska et al.,
LAI
Partitioning
factors
Tubers
SLA
Roots
Stems
Leaves
F. 1. Schematic representation of the crop growth model in which the
main processes are light interception, conversion to dry matter and
assimilate allocation.
1984). This led to the model as summarized in Fig. 1, which
is based on the model described by Spitters and Schapendonk (1990). Crop-water relations were not included and
the parts dealing with dry matter allocation and leaf
senescence were replaced by the equations given below.
Dry matter production was calculated from the amount
of photosynthetically active radiation intercepted by the
canopy and its conversion efficiency for dry matter
production. The light-use efficiencies (Table 1) were estimated from field data with the help of the model, by
minimizing the sum of squares of the differences between
measured and calculated total biomass at the periodic
harvests (Klepper and Rouse, 1991).
Assimilate allocation
The model calculations of the fraction of total dry matter
produced allocated to the tuber, were based on the
assumption that the tubers are the dominant sink in the
potato crop. Three phases of dominance of the tubers can be
distinguished ; the initial phase when tuber growth is sinklimited ; the second phase when there is competition for
assimilates between tubers and other organs, and the third
phase when tubers are such a strong sink that all assimilates
are allocated to them.
The potential sink strength of the tubers (Ptb) is described
by their size (Wtb) and their maximum relative growth rate
(Rtb) which is influenced by the effect of temperature (Etb) as
described by eqn (1a).
Ptb ¯ Wtb Rtb Etb t & TI
(1a)
Kooman and Rabbinge—Tuber Dry Matter Allocation and Potato Crop Earliness
237
T     1. Light-use efficiency (LUE ; g MJ−"), emergence day (d ), tuber initiation day (d ), days between emergence and tuber
initiation (d ) and leaf duration (°Cd ) as estimated from the experiments for the Šarieties used in the two sets of experiments
LUE g MJ−"
Set 1 1968
1969
Average
Set 2 1971
1972
1973
Average
Prudal
Mentor
Alpha
Irene
Pimpernel
Prudal
Mentor
Alpha
Irene
Pimpernel
Prudal
Mentor
Alpha
Irene
Pimpernel
Ostara
Rheinhort
Alpha
Condea
Ostara
Rheinhort
Alpha
Condea
Ostara
Rheinhort
Alpha
Condea
Ostara
Rheinhort
Alpha
Condea
3±2
3±5
3±4
3±1
3±2
2±4
2±4
2±3
2±2
2±1
2±8
3±0
2±9
2±7
2±7
2±5
2±5
2±6
2±3
2±5
2±4
2±5
2±2
1±9
1±9
2
1±8
2±3
2±3
2±4
2±1
Emergence
day
128
128
130
129
131
125
126
128
126
128
126±5
127
129
127±5
129±5
134
132
136
135
128
133
135
133
135
136
139
136
132
134
137
135
The effective temperature function for tubers is taken from
Heemst (1986) and normalized between 0 and 1. In the
initial phase when tubers are still small and where growth is
sink-limited, the growth rate of tubers is equal to their
potential sink strength. The second phase of tuber growth is
characterized by competition for assimilates between tubers
and the rest of the plant. Tubers in this phase are not a
sufficiently strong sink to acquire all the assimilates they
require to maintain their exponential growth. The source
(availability of assimilates) is too small to enable all organs
to grow at their potential rate. If it is assumed that the
competition increases with increased potential sink strength
of the tuber, the daily allocation of dry matter to the tubers
( ftb) can be described by eqn (1b).
ftb ¯
Ptb
∆W­Ptb
(1b)
When eqn (1a) is substituted in eqn (1b), eqn (1c) is
obtained.
Wtb Rtb Etb
(1c)
ftb ¯
∆W­Wtb Rtb Etb
The result is one equation which describes all phases of dry
matter allocation to the tubers. Initially Ptb is very small
compared to ∆W and tuber growth approaches exponential
growth. Gradually Wtb increases, resulting in a greater sink
Tuber initiation
day
148
150
156
160
165
140
147
149
149
154
144
148±5
152±5
154±5
159±5
149
149
159
162
153
159
168
169
150
153
158
161
151
154
162
164
Emergence to
tuber initiation
Leaf longevity
°Cd
20
22
26
31
34
15
21
21
23
26
17±5
21±5
23±5
27
30
15
17
23
27
25
26
33
36
15
17
19
25
18
20
25
29
1100
1400
1500
1200
1500
1100
1500
1600
1400
1600
1100
1450
1550
1300
1550
1200
1200
1600
1500
1000
1000
1500
1600
1000
1000
1700
1600
1067
1067
1600
1567
strength and competition between tubers and foliage. Finally
when Wtb becomes very large ftb approaches 1 and all
assimilates are allocated to the tubers.
The maximum relative growth rate for tubers used in this
study (0±37 d−") was derived by Ingram and McCloud (1984)
from experiments in Florida, USA. The value they reported
is slightly higher than the highest values of whole plants of
wild plant species and crops as reported by Poorter and
Remkes (1990) and Potter and Jones (1977). The use of the
relatively high value of 0±37 d−" is justified by the fact that
tubers consist of compounds with a more favourable
conversion coefficient compared to whole plants.
Assimilates not partitioned to the tuber are allocated to
the shoot and divided between the leaves and stems [eqns (2)
to (4)]. In the model, root biomass is ignored because root
measurements in the field experiments were not sufficiently
accurate.
(2)
fsh ¯ 1®ftb
flv ¯ [ flv ®(α ftb)] fsh
!
fst ¯(1®flv) fsh
(3)
(4)
Where f is the fraction of total daily growth allocated to an
organ and the subscripts lŠ, sh and st represent leaves, shoot
and stems respectively. flv is the initial partitioning to the
!
leaves and α is the slope of the partitioning within the shoot.
Leaves are assumed to be more sensitive to competition for
238
Kooman and Rabbinge—Tuber Dry Matter Allocation and Potato Crop Earliness
the tubers than stems, therefore, a tuber dependent term is
included in eqn (3). Based on the 1968 data the value of flv
!
was set at 0±75 and the value of α was set at 0±5.
Light interception was calculated from the leaf area
index, calculated as the product of leaf dry weight and its
specific leaf are (Spitters and Schapendonk, 1990). The
moment at which leaves senesced was dependent on
temperature and self-shading [eqn (5)].
∆Wld ¯ Wlv,i
or
3
1.0
Fraction
Light interception, critical LAI and maximum leaf
longeŠity
A
0.0
125
3 tlv,i & Tlv
if
0LAI®LAI
1R
LAI
cr
sh
&1
0.5
150
175
200 225
Time (d)
250
275
300
(5)
cr
B
1.0
Fraction
where ∆Wld is the daily increase of dead leaves ; Wlv,i the
weight of leaves formed on day i, henceforth referred to as
daily leaf class ; tlv,i effective temperature (°C) for the daily
leaf class i ; Tlv the leaf longevity in °Cd ; LAI the leaf area
index ; LAIcr the critical leaf area index and Rsh (d−") the
relative death rate due to shading. When the temperature
sum of a daily leaf class exceeded the leaf longevity, the
leaves in that leaf class are considered dead or when the LAI
exceeds the critical LAI the oldest leaves die after 10–20 d,
dependent on the actual LAI [eqn (5)]. This critical LAI was
set at 7±5 on the basis of the 1968 data. The Rsh (d−") was also
derived from these data. Leaf longevity was derived with the
help of the simulation model. The leaf longevities given in
Table 1 were acquired by first calculating the light interception over the growing season from the measured amount
of leaf dry matter and the specific leaf area. Subsequently
the leaf longevity was set at the value that minimized the
difference between the calculated and measured duration of
the light interception.
0.5
0.0
125
150
175
200 225
Time (d)
250
275
300
F. 2. Fraction of the daily assimilate production allocated to the
tubers in 1968 (A) and 1972 (B). Observed values for an early variety
(^) (1968, Prudal and 1972, Ostara) a late variety (_) (Alpha) and the
simulated values parameterized according to Table 1 for early (— —)
and late (——) cultivars.
RESULTS
Parameter estimation
The Julian day numbers at plant emergence and tuber
initiation were estimated from the growth curves of the field
experiments of set 1 and set 2. The emergence date varied
between days 128 and 139 (Table 1). The time of tuber
initiation also varied between the years. The difference
between 1968 and 1969 was 10 d in set 1 and in set 2 there
was a maximum difference of 11 d (Table 1). The time
between emergence and tuber initiation differed markedly
between years. In set 1 the time between emergence and
tuber initiation was longer in 1968 than in 1969 and in set
2 this time was longer in 1972 than in 1971 or 1973. In all
experiments, cultivars classified as early in the Netherlands
List of Recommended Cultivars (1968–1976) also showed
the earliest tuber initiation.
The light-use efficiencies differed between years and
cultivars. In agreement with Spitters (1987), it was found
that the difference in light-use efficiency between years was
larger than between cultivars within a given year. This may
be partly attributable to the differences in rainfall, resulting
in a relatively low light-use efficiency in the dry years 1973
and 1969,
Leaf longevity was cultivar-dependent and systematically
shorter (up to 700 °Cd) in early cultivars than in late
cultivars.
Performance of the model
The total dry matter production part of the model had
been validated in previous studies (e.g. Spitters, 1987, 1990).
The dry matter distribution and leaf senescence sections
were new in the model and investigated for the first time in
the present study. The parameters estimated in the previous
section and summarized in Table 1 were used to simulate the
different experiment–cultivar combinations. Because there
were many experiment–cultivar combinations in this study
Kooman and Rabbinge—Tuber Dry Matter Allocation and Potato Crop Earliness
A
Fraction
1.0
0.5
0.0
125
150
175
200
225
Time (d)
250
275
300
B
Fraction
1.0
0.5
0.0
125
239
Figure 2 shows the comparison of the observed fraction of
dry matter produced allocated to the tubers between two
consecutive harvests, and the simulated daily allocation.
The simulation of early and late cultivars in both set 1 (Fig.
2 A) and set 2 (Fig. 2 B) corresponded well with the
measured values and justifies the conclusion that the relation
given in eqn (1c) performed well for the given conditions.
Even Alpha grown in 1968, in which the tuber dry matter
production was simulated worse than for the other cultivars,
had a dry matter allocation that simulated the measured
values closely (Fig. 2 A).
Figure 3 A and B shows the comparison of the observed
light interception and the simulated values for set 1 and set
2. The simulation of leaf growth and LAI increase apparently
agreed well with the experimental data. For each cultivar a
constant value was taken for the leaf longevity, and no
distinction was made between leaves formed early or late in
the season. For the early cultivars this constant value
simulated the decrease of LAI well (data not shown). For
the late cultivars, however, the longevity of individual leaves
differed considerably, leading to the LAI at the end of the
season being overestimated. This did not influence the
simulation of the total production (Table 2), because the
predicted time of crop senescence, a major determinant of
productivity, was close to that observed and light interception mainly takes place in the uppermost four leaf
layers (Haverkort et al., 1991).
SensitiŠity analysis
150
175
200
225
Time (d)
250
275
300
F. 3. Light interception during the season in 1968 (A) and 1972 (B).
Observed values for an early variety (^) (1968, Prudal and 1972,
Ostara) a late variety (_) (Alpha) and the simulated values
parameterized according to Table 1 for early (— —) and late (——)
varieties.
only a selection is shown in Figs 2 and 3. A more complete
list of the model performance is given in Table 2. In this
table the simulated values are compared with measured
values in the field. The simulated combinations of cultivar¬
location were not included in the parameterization of the
model. In Figs 2 and 3 data on an early and a late cultivar
of both experimental sets are given. The early cultivar in set
1 was Prudal (1968) and in set 2 it was Ostara (1972), the
late cultivar in both sets was Alpha (1968, 1972).
Table 2 shows that the tuber dry matter was predicted
well. In most cases the average difference between simulated
and measured was less than 20 %. Only late cultivars in 1968
had a larger difference. This large difference is attributable
to reallocation at the end of the growing season (which is
not included in the model) since the dry matter allocation
and total growth for these cultivars was simulated well.
The influence of the maximum leaf longevity, tuber
initiation day and maximum relative growth of tubers (Rtb)
on crop earliness were evaluated by varying them in the
model for a standard early and a standard late cultivar. The
early cultivar was defined by tuber initiation at day 144 and
a leaf longevity of 1100 °Cd. For the late cultivar these
values were day 160 and 1500 °Cd. Weather data were the
daily average values of solar radiation, minimum and
maximum temperatures at Wageningen from 1960 to 1990.
The emergence date of the crop was set to be 10 May and
the season lasted until the fraction of light intercepted was
reduced to zero or until 31 Dec. at the latest. The light-use
efficiency was set at 2±7 g MJ−" PAR and plant density was
4¬10% plants ha−".
For the evaluation, crop earliness was divided into two
components : leaf growth and leaf senescence. Leaf growth
occurs in the period between emergence and the moment
when leaf growth stops, defined here as the day on which
90 % of the daily assimilate production is allocated to the
tubers (D ). After this day no substantial leaf growth
*!
occurs. The timing of leaf senescence can be evaluated by
the moment when crop growth stops, defined as the moment
at which the fraction light intercepted is reduced to 50 % of
full light interception (D ) ; after this day no marked
&!
production takes place.
Tuber initiation and leaf longevity were varied between
the minimum and maximum values in the experiments
(Table 1). The relative tuber growth rate in the experiment
was only affected by temperature, although when growing
conditions were less optimal this is not necessarily the case.
240
Kooman and Rabbinge—Tuber Dry Matter Allocation and Potato Crop Earliness
320
A
T     2. Goodness of fit defined as o1}n Σnk= (s®m}m)#
"
where n is the number of harŠests, s the simulated Šalue, m the
measured Šalue for tuber dry matter, total dry matter and
light interception of the crop
Day of year
280
Set 1 1968
240
1969
200
160
140
145
150
155
160
Tuber initiation (d)
165
170
Set 2 1971
1972
360
B
1973
Day of year
310
Total dry
matter
Light
interception
0±22
0±33
0±34
0±19
0±37
0±27
0±25
0±21
0±20
0±20
0±18
0±09
0±19
0±19
0±27
0±19
0±13
0±21
0±09
0±12
0±08
0±08
0±17
0±26
0±17
0±13
0±19
0±15
0±14
0±14
0±14
0±15
0±14
0±12
0±14
0±16
0±13
0±08
0±11
0±10
0±09
0±11
0±10
0±12
0±03
0±14
0±09
0±01
0±09
0±02
0±02
0±01
0±02
0±01
0±06
0±07
0±09
0±00
0±03
0±02
0±01
0±01
0±10
0±05
0±04
0±03
260
210
160
1000
1200
1400
Leaf longevity (°Cd)
1600
360
C
310
Day of year
Prudal
Mentor
Alpha
Irene
Pimpernel
Prudal
Mentor
Alpha
Irene
Pimpernel
Ostara
Rheinhort
Alpha
Condea
Ostara
Rheinhort
Alpha
Condea
Ostara
Rheinhort
Alpha
Condea
Tuber dry
matter
260
210
160
0.0
0.1
0.2
0.3
rgrtb(d–1)
0.4
0.5
0.6
This parameter was varied between 0±1 and 0±6 d−" to
ascertain its effect.
The results of the sensitivity analysis for tuber initiation
are given in Fig. 4 A, with the value of the parameter on the
abscissa and the Julian day number of D and D on the
*!
&!
ordinate. Figure 4 B shows the effect of leaf longevity, and
Fig. 4 C shows the effect of maximum relative growth rate.
When tuber initiation was delayed, leaf growth was
prolonged, resulting in a later crop (Fig. 4 A). The tuber
initiation dates studied ranged from day 140 to day 169.
This range of 29 d was also found again in D and D . The
*!
&!
early and late cultivars reacted similarly, indicating that
with a fixed leaf longevity a delay of 1 d in tuber initiation
date results in a delay of 1 d in crop senescence date.
Leaf longevity (Fig. 4 B) did not affect leaf growth,
resulting in a horizontal line for D in both the early and
*!
the late cultivar, with a difference of 16 d caused by the
difference in tuber initiation. The influence of leaf longevity
on D is large. When leaf longevity is increased from 1000
&!
to 1700 °Cd there was a shift in D of 65 d for the early
&!
cultivar and of 68 d for the late cultivar. The additional 3 d
for late cultivars resulted from its growing later in the
season under lower temperatures.
F. 4. The effect of tuber initiation date (A), leaf longevity (B) and
relative tuber growth rate (C) on the day that 90 % of the daily
assimilate production is allocated to the tubers (D ) in a standard early
*!
(— - — - —) and a late ([[[[[[) variety and on the day that the light
interception is reduced to 50 % (D ) in an early (— —) and a late
&!
(——) variety. Values for the standard early (D) and late (*) variety
are given in the figures.
Kooman and Rabbinge—Tuber Dry Matter Allocation and Potato Crop Earliness
The relative tuber growth rate can influence crop earliness
more than the other two factors (Fig. 4 C). Moreover, the
nature of the reaction is different. With tuber initiation and
leaf longevity the reaction is constant and has an equal
sensitivity over the whole range. Crop earliness is sensitive
to a change in Rtb when Rtb lies between 0±1 and 0±3, and is
less sensitive at values of Rtb above 0±4. The small values are
found when growing conditions for tubers are sub-optimal.
The Rtb mainly affects leaf growth which even continued
until the end of the season at Rtb values below 0±2 d−".
DISCUSSION
The simplicity of the model used here has the advantage that
all processes can be verified easily and that information in
the model is accessible to the reader (Spitters, 1990). Despite
its simplicity, the model enabled the central processes such
as light interception and assimilate allocation to be studied
in relation to each other and to the environmental factors.
Crop earliness can be divided into two components. The
first component, leaf growth, is the result of crop growth
and the allocation of assimilates to the leaves. The second
component is the longevity of the formed leaves. It appears
that factors which influence the strength of the tuber sink
affect both assimilate allocation and the leaf longevity.
Assimilate allocation
The tuber sink strength in the initial growth phase is
determined by the weight of the tubers, a result of their time
of initiation, initial weight and relative growth rate (Engels
and Marschner, 1986). The growing conditions were nearly
optimal and, therefore, the relative growth rate was assumed
to be at its maximum and did not affect the earliness of the
crop directly. For the simulations the maximum value of Rtb
was assumed to be constant. This maximum was altered by
the effective temperature. This meant that tuber growth was
determined by temperature and assimilate availability.
Besides the maximum relative growth rate, initial tuber
weight was also assumed to be constant. The variation in
assimilate allocation is therefore determined by the time of
initiation only, which on its own is a relatively insensitive
parameter with respect to assimilate allocation and consequently to crop earliness (Fig. 4 A). On the other hand,
relative growth rate can have a large influence on the
assimilate allocation of a crop, especially when a crop is
grown under sub-optimal conditions and the value of Rtb is
low (Fig. 4 C). This is probably why crops with a mild water
stress at the beginning of the growing season persist longer
(Loon, 1981) or why a mulched crop under above-optimal
temperatures dies sooner than an unmulched crop (Midmore, 1988).
Leaf longeŠity
The simulation of assimilate allocation could explain part
of the variation in crop earliness. The rest of the variation
was the result of a systematic increase in leaf longevity, up
241
to 700 °Cd (Table 1) of late cultivars. This explained most of
the variation in crop earliness ; a small part was explained by
the change in tuber initiation date and tuber growth in the
sink-limited phase (i.e. the phase before D ). In the sensi*!
tivity analysis, D was shifted 29 d for a standard cultivar by
&!
changing the tuber initiation date. However, when the leaf
longevity was lengthened from 1000 to 1700 °Cd, D was
&!
65 d later for an early cultivar and 68 d for a late cultivar,
so the change in longevity seems more important. The
differences in crop earliness found here correspond with
experimental data for early cultivars that senesced in midAug. and for very late cultivars that senesced at the end of
Oct. Late cultivars had a leaf longevity of about 1500–
1700 °Cd, or about 110 d. Vos and Biemond (1992) found
similar values in a greenhouse experiment with the mid-late
cultivar Bintje well supplied with nitrogen. When leaves do
not attain the maximum longevity, factors other than
temperature shorten their life span. The relation between
crop earliness and leaf longevity suggests that the sink
strength of the tubers not only limits the production of
leaves but also their longevity.
Harris (1983) postulated that in the internal competition
between the different organs of the crop the tuber is the
dominant sink and that roots are the first to be subjected to
this competition, causing root growth to decrease, which
results in a concomitant reduction in the uptake of nutrients,
especially nitrogen. A shortage of nitrogen is involved in the
senescence of the crop. Considerable reallocation of carbon
(Moorby, 1970) and nitrogen (Millard, Robinson and
Mackie-Dawson, 1989) from the foliage to the tubers at the
end of the growing season has been found under experimental conditions. It is assumed that, at the end of the
season when the rooting zone is depleted, tubers withdraw
nitrogen from the foliage. This reallocation will exhaust the
nitrogen pool in the foliage faster in an early cultivar with
a smaller amount of foliage than in a late cultivar with a
larger amount of foliage. In early cultivars this will result in
a shorter leaf longevity. Such a process, called self
destruction, has also been described by Sinclair and De Wit
(1976) in soybean.
This study supports the self destruction hypothesis in
several ways. Firstly, because we found that early cultivars
have a shorter leaf longevity than late cultivars, secondly
because of the variability in the individual leaf longevity in
late cultivars. The lower leaves in the canopy of late
cultivars senesce faster than simulated with the model in
which leaves have a fixed longevity and it is precisely these
lower leaves that are influenced first by reallocation. Both
phenomena can be attributed to redistribution of nitrogen
to the tuber. A third argument in favour of the hypothesis
is that fast growing crops have a shorter leaf longevity than
slower growing crops (Table 1). In fast growing crops tubers
grow faster and therefore need more nitrogen at the expense
of leaves, thus reducing the leaf longevity.
In conclusion, the tuber initiation date in itself is not the
only factor determining crop earliness. In this study the
effect of tuber sink strength on leaf longevity was more
important to crop earliness. This suggests that more study is
needed of the relation between nitrogen uptake and
distribution and the earliness of a potato crop.
242
Kooman and Rabbinge—Tuber Dry Matter Allocation and Potato Crop Earliness
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APPENDIX: LIST OF SYMBOLS
Symbol
α
∆W
∆Wld
∆Wlv
fj
flv
fsh
fst
ftb
LAI
LAIcr
Rtb
Rsh
tlv
tlvmax
ttb
Wlv,i
Meaning
Slope of partitioning within shoot
Daily total growth
Increase of weight of dead leaves
Leaf growth rate
Fraction allocated to organ j
Fraction allocated to leaves
Fraction allocated to the shoot
Fraction allocated to stems
Fraction of total dry matter
partitioned to the tubers
Leaf area index
Critical LAI for self shading
Relative growth rate of tubers
Death rate of leaves due to self
shading
Effective shoot temperature
Maximum leaf longevity for a daily
leaf class
Effective tuber temperature
Weight of daily leaf class i
Units
—
kg ha−" d−"
kg ha−" d−"
kg ha−" d−"
—
—
—
—
—
—
—
d−"
d−"
°C
°Cd
°C
kg ha−"